TY - JOUR

T1 - Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains

AU - Balint, Peter

AU - Lin, Kevin K.

AU - Young, Lai Sang

N1 - Funding Information:
Research partially supported by OTKA (Hungarian National Research Fund) grants: F 60206 and K 71693; and by the Bolyai scholarship of the Hungarian Academy of Sciences.
Funding Information:
Research partially supported by NSF Grant DMS-0600974.

PY - 2009/1

Y1 - 2009/1

N2 - We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.

AB - We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.

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U2 - 10.1007/s00220-009-0918-x

DO - 10.1007/s00220-009-0918-x

M3 - Article

AN - SCOPUS:72249106501

SN - 0010-3616

VL - 294

SP - 199

EP - 228

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -